Topics in Nonconvex Optimization

Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions. Nonconvex optimization problems are frequently encountered in modeling real world systems for a very broad range of applications including engineering, mathematical economics, management science, financial engineering, and social science. This contributed volume consists of selected contributions from the Advanced Training Programme on Nonconvex Optimization and Its Applications he.

9.2 Preliminaries.

Foreword; Preface; Contents; List of Contributors; Chapter 1; Some Equivalences Among Nonlinear Complementarity Problems, Least-Element Problems, and Variational Inequality Problems in Order; 1.1 Introduction; 1.2 Preliminaries; 1.3 Equivalence of Nonlinear Complementarity Problems and Least-Element Problems; 1.4 Equivalence Between Variational-Like Inequality Problem and Least-Element Problem; 1.5 Equivalence Between Extended Generalized Complementarity Problems and Generalized Least-Element Problem.

1.6 Equivalence Between Generalized Mixed Complementarity Problems and Generalized Mixed Least-Element ProblemReferences; Chapter 2; Generalized Monotone Maps and Complementarity Problems; 2.1 Introduction; 2.2 Preliminaries; 2.3 Different Types of Generalized Monotone Maps; 2.4 Generalized Monotonicity of Affine Maps; 2.5 Generalized Monotone Affine Maps on; and Positive-Subdefinite Matrices; 2.6 Generalized Positive-Subdefinite Matrices; References; Chapter 3; Optimality Conditions Without Continuity in Multivalued Optimization Using Approximations as Generalized Derivatives.

3.1 Introduction and Preliminaries3.2 Firstand Second-Order Approximations of Multifunctions; 3.3 First-O…